Question

A bank wishes to estimate the mean balances owed by customers holding MasterCard. The population standard deviation is estimated to be $500. If a 97 percent confidence interval is used and an interval of $100 is desired, how many cardholders should be sampled?

Answer 1

Answer: 471

Explanation:

Given : The population standard deviation is estimated to be $500.

i.e .
`\sigma=\$500`

If a 97 percent confidence interval is used and an interval of $100 is desired.

i.e. Margin of error = half of interval

i.e. E=
`(\$100)/(2)=\$50`

Significance level : 1-0.97=0.03

Critical value for 97% confidence interval :
`{z_(\alpha/2)=z_(0.03/2)=2.17`

Formula for sample size :

`n=((z_(\alpha/2)\ \sigma)/(E))^2\\\\=((2.17*500)/(50))^2\\\\=470.89\approx471`

Hence, at-least 471 cardholders should be sampled.